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KTH Royal Insistute of Technology

School of Engineering Sciences in Chemistry,Biotechnology and Health

Master thesis:

Simulation of dry matter loss in biomass storageDate: 2019-06-24

Author: Jens Bjervas1, bjervas@kth.se

Supervisors: Matthaus Babler2, Erik Dahlen3

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1Master student at the department of Chemical Engineering, KTH2Associate professor at the department of Chemical Engineering, KTH3Research and development manager at Stockholm Exergi

Contents1 Scope and aims 1

1.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Specific research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Method & methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Background 22.1 Storage of biomass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1.2 Degradation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Modeling 53.1 Microbial activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Chemical oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Physical transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.5 All processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.6 The general case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.6.1 Case 1 - ’Deep inside the stack’ (No boundary effects) . . . . . . . . . . . . . . . . . . 133.6.2 Case 2 - ’Endless depot of oxygen’ (Constant optimal oxygen concentration) . . . . . . 14

4 Results and discussion 154.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 Future work 23

6 Conclusions 24

7 Appendices 257.1 Appendix A - Biological degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7.1.1 Dry matter degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257.1.2 Heat generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7.2 Appendix B - Chemical oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347.2.1 Material degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7.3 Appendix C - Physical transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367.4 Appendix D - All processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.4.1 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.5 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397.6 Appendix E - Field study result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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Foreword

I would like to begin this report by giving a big thanks to Matthaus Babler, Erik Dahlen and Erik Anerudfor their support and invaluable contribution to the project.

Abstract

Material degradation and a decrease of fuel quality are common phenomena when storing biomass. AMagnitude of 7.8% has been reported to degrade over five months when storing spruce wood chips inthe winter in Central Europe. This thesis presents a theoretical study of biomass storage. It includesinvestigations of bio-chemical, chemical and physical processes that occur during storage of chipped woodybiomass. These processes lead to degradation caused by micro-activity, chemical oxidation reactions andphysical transformation of water. Micro-activity was modeled with Monod kinetics which are Michaelis-Menten type of expressions. The rate expressions were complemented with dependency functions describingthe impact of oxygen, moisture and temperature. The woody biomass was divided into three fractions.These fractions represent how hard different components of the wood are to degrade by microorganisms.Chemical oxidation was modeled as a first order rate expression with respect to the active components of thewood. Two different cases have been simulated during the project. Firstly, an isolated system with an initialoxygen concentration of air was considered. This case displayed a temperature increase of approximately2◦C and a material degradation less than 1%. The second case considered an isolated system with anendless depot of oxygen. This case resulted in degradation losses around 0.45-0.95% in the temperaturerange between 65-80◦C during approximately 300 days of storage. The temperature increased slowly due tochemical oxidation.

Nomenclature

Table 1: Quantities, descriptions and units used in the simulations.

Quantity Description Unitρ Density kg/m3

ρSHHard to degrade fraction of substrate (makro-molecules) kg/m3

ρSEEasy to degrade fraction of substrate (extractives) kg/m3

ρSIInert fraction of substrate kg/m3

ρm Active microorganisms kg/m3

ρd Dead microorganisms kg/m3

ρO2Oxygen kg/m3

ρCO2 Carbon dioxide kg/m3

ρN2Nitrogen kg/m3

ρ(W,L) Liquid water kg/m3

ρ(W,V ) Water vapor kg/m3

M Molecular weight g/molecp Specific heating value kJ/(kg ·K)

∆H Specific entalphy kJ/kgp Pressure PaT Temperature KR Gas constant J/(mole ·K)r Reaction rate kg/(m3 · s)α Weight fraction in bio-chemical reaction path -k1 Rate constant s−1

KS1Saturation constant -

k2 Rate constant s−1

KS2 Saturation constant kg/m3

k3 Rate constant s−1

ω Weight fraction -ν Stoichiometric coefficient -k0 Pre-exponential factor s−1

EA Activation energy J/moleA Antoine constant -B Antoine constant -C Antoine constant -f Conversion factor (kg · Pa)/(g ·mmHg)

S Heat source kJ/(m3 · s)Q Heat transport kJ/(m3 · s)D Diffusion coefficient m2/sµ Dynamic viscosity Pa · sβ Permeability coefficient m2

Chapter 1 - Scope and aims

1.1 Aim

The aim of this thesis was to develop a mathematical model to predict dry matter losses related to large-scalestorage of chipped woody biomass. The total material loss is the sum of biological degradation, chemicaloxidation and physical transformation e.g. condensation and evaporation of water. For this, an originalmodel based on differential mass and energy balances was developed. Two limiting cases were considered.Case 1 was isolated system with an initial oxygen concentration of air while the second case was an isolatedsystem with an endless depot of oxygen. The simulations were done in MATLAB version 2018a usingstandard ode solvers. This master thesis was done at KTH and Stockholm Exergi in cooperation SLU.

1.2 Specific research questions

The project addressed three specific research questions.

• How to model degradation caused by biological, chemical and physical processes?

• How do the different processes interact with each other, and which ones are the most crucial in con-trolling material loss?

• Can the model predict thermal runaway?

1.3 Method & methodology

The process of biomass degradation is slow. A theoretical study is therefore suited to investigate the problem.The created model involves biochemical, chemical and physical processes. The individual components weretheoretically and numerically investigated individually before all elements were combined. A uniform smallvolume element have been considered. This volume element have been exposed to different conditions tosimulate different cases. The model was compared to data from field studies in order to show its validityand understand its limitations.

1.4 Delimitations

This project was delimited to 20 weeks. There are several types of biomasses that may be used in industrialprocesses which all have unique physical properties. Stockholm Exergi uses forests logging residues in theirboilers. Norway spruce is largely present in forest residues from Nordic countries and this work has thereforebeen delimited to Norway spruce as the principle biomass. [1] Data from field studies have been taken fromNykvarn, Sweden. The field study were conducted between February to August in 2017 by Erik Anerud,who kindly provided the raw data which is included in this project.

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Chapter 2 - Background

2.1 Storage of biomass

2.1.1 Overview

EU targets reduced greenhouse gas emissions by 40% compared to 1990 by 2030. An increased utilization ofrenewable energy sources such as biomass needs to be applied to reach the global energy and environmentalgoals set for the coming future. [2] Biomass may be used for conventional combustion in combined heat andpower plants, which is the case at Stockholm Exergi. The effective heating value of biomass varies but can bearound 20 MJ/kg dry basis. [3] An important industrial process for biomass is biomass gasification. Biomassgasification produces products which can be used in various applications such as heat and power production.The gasification process is a thermochemical process that generally involves the following steps: drying,pyrolysis, partial combustion and gasification. Pyrolysis is the process of thermally decompose carbonaceousbiomass under anaerobic conditions. Common products from pyrolysis are charcoal, oils and syngas. [4]Biomass is usually harvest at specific times of the year and often contains a high moisture level after harvest.A high water content lowers the net calorific value since a lot of energy is spent to evaporate water. [5] Itis necessary to have large scale storage facilities for biomass for two major reasons. These reasons are to letthe material dry and to match periods of high demands. Biomass comes in a variety of forms and from avarietry of places. Forest residuals also known as GROT is often used in Sweden. The moisture content infresh forest residues is usually around 40-55 wt% dry basis. [6] Material degradation and heat generationare commonly observed in stored stacks of chipped wood. [7]

Forest residuals are made up by a matrix of materials such as bark, needles, sapwood, heartwood andinorganic matter. The ratio of these materials depends on the harvest site. The three major componentsof wood are cellulose, hemicellulose and lignin. There is also a small portion of smaller sugar units presentin fresh GROT. The low mass to volume ratio of forest residuals makes transporting and storing relativelycostly and it is thus important to understand the storage behaviour to optimize storage conditions. Forestresiduals are chipped in order to compress the material for storage and transport. Uncominuted GROTtypically cannot be transported for longer distances than 40 kilometers if it is to be economicaly viable.Chipped GROT can be transported for longer distances but chipping also increases the risk of energy lossesduring storage. Energy losses occur both due to quality degradation and the direct loss of material itself. [6]Material loss is caused by vaporization of water, living cell respiration, biological degradation and chemicaloxidation reactions. [3] The dry matter composition, ash content and moisture content all affect the heatingvalue and thereby fuel prices. [5] Biomass storage can be designed in a variety of ways with ranging costs.Uncovered open air storage is the cheapest option but generally has the highest material loss and qualitydegradation, while covered storage with climate control costs most but tends to retain higher quality andgives rise to less material loss than other alternatives. Which storage system to chose consequently dependson a lot of parameters such as type of biomass to be stored, geometry and storage time, quantity to bestored, precipitation, wind, transportation distance, end usage etc. [7]

Many studies uses net-bags to measure dry matter (DM) losses. These bags are filled with wood substrateand distributed inside the biomass pile. The moisture content and weight is measured and compared beforeand after storage. Hofman et al. performed field experiments in south Germany in 2018. Here, sprucewood chips were stored between November of 2014 to 2015 of April as well as between May to October in2015. Two piles of around 200 m3 were built in each storage period. One pile was covered with nonwovenpolypropylene fleece while the other pile was kept uncovered. Degradation measurements were done byplacing 144 balance bags inside each pile. After five months of summer storage, 11.1 % had degraded in thecovered pile while 7% DM degraded in the uncovered pile. In the winter, 8% was degraded in the coveredpile while 7.8% was degraded in the uncovered pile. [8]

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Another problem in biomass storage is the self-heating that goes along with the previously mentioned mech-anisms that causes material loss. Microbial activity, chemical oxidation reactions and adsorption of waterproduces heat. The heat transfer inside and from a biomass stack is limited which causes a rise in tempera-ture. [3] The self-heating process may lead to self-ignition which can lead to fires. There have been multiplereports of self-ignited fires. For example in Arlov, Sweden a pile of wood chips caught fire in 2011. [9]

One solution to reduce DM losses during storage and terminate the risk of self-ignition could be to addchemical additives which reduces microbial activity into the storage pile. A study on chemical additiveswas performed in 1973 by Wallace E. Eslyn. Thirty different addiatives were investigated with incubationtests on red pine. Several chemicals were evaluated as successive in reducing microbial activity. However,the additives effect on the thermal oxidation reaction in the boiler also have to be considered. Most of theinvestigated chemical substances would result in undesired oxidation reactions. [10]

2.1.2 Degradation mechanisms

Living cell respiration

Living cell respiration is the name of the automotive catabolic process that converts glucose into ATP inplants. This reaction involves several steps but the net heat released from the overall process is 1100 kJ/mol.Temperatures around 60◦C terminates the reaction by inactivating enzymes involved in cell respiration. Thisprocess is short lived in chipped piles, where it can prolong between 10 and 40 days. [3]

Biological degradation

There are various microorganisms and bacteria that can degenerate wood. However, the mobility of bacteriais limited to transport in liquid water since they expand by cell division. The degradation by bacteria istherefore less of a problem than degradation by other wood-decaying organisms. The biological degradationof wood is caused by enzymes introduced by wood consuming organisms. The enzymes transform insolublemolecules to soluble chemical substances that are used in the metabolism in these organisms. There are afew well known families of fungus that may colonize wood, two of these are Brown-rot and White-rot fungi.Brown-rot usually prefers soft-wood while White-rot usually prefers hard-wood. Brown-rot mostly degradepolysaccharides but they also break down lignin to a lesser degree. White-rot fungi degrades all of the majorcomponents of wood but has a preference to lignin. [11] A portion of degraded substrate is used to grownew fungi while the rest is used in metabolism. [12]

The biological degradation rate caused by microorganism is dependent on the present moisture and oxy-gen content as well as on the temperature. Different microorganisms operate during different temperaturewindows. The activity of wood-decaying microorganisms is terminated around 60-65◦C. [3] Yu Fakasawainvestigated the growth rate of Brown-rot and White-rot fungi species in Pinus densiflora deadwood in thetemperature span of 5-40◦C. It was concluded that Brown-rot fungi have optimum growth rates at around30◦C while White fungus show optimum rates between 20-30◦C. [13] Almost all microbial activity only oc-curs if the water content is above the fiber saturation point (around 20-25 wt%) as fungi require water togrow. If the moisture content gets to high the degradation slows down since the oxygen solubility in water isquite low. Measuring the effect of moisture is hard since moisture gradients exists within the wood and sinceit is difficult to keep the water content constant over long periods. [14] Microbial activity occurs in bothaerobic and anaerobic conditions. Aerobic degradation goes faster and causes emissions of carbon dioxideand carbon monoxide. [3] Methane, alcohols and organic acids are produced in anaerobic conditions. [15]The heat production is less under anaerobic conditions. [16]

In 2011, Ferrero et al. published results from temperature and gas measurements from various positionsinside a heap of pine wood, the dimensions of the stack were 20 × 15 × 6 m3. Their experiments showeda steep increase in temperature inside the heap within the first 10-20 days. The authors suggested thatthe fast initial increase in temperature is caused by consumption of free sugar species that become largely

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available after chipping. The free sugars can be consumed by a larger population of microbial speciesthan the cellulose, hemicellulose and lignin. This would result in a decrease in heat generation once theeasily degradable portion is consumed. Furthermore, emissions of methane was recorded on up to 60 ppmv,indicating very little fermentation inside the stack. The inner temperature in the stack decreased whenthe other layer froze. An explanation could be that the oxygen diffusion into the pile was hindered whichcaused a decrease in microbial activity. [17] Whittaker et al. did a similiar study. Measurements of methaneemissions reached a peak around 400 ppmv after 40 days. This occurred after the first spike of carbondioxide, indicating anaerobic conditions inside the pile. All measured emissions reached a baseline after 60days, the carbon dioxide emission were below 5000 ppmv while the methane production were below 50 ppmv.[18]

Thermal degradation and chemical oxidation reactions

Chemical oxidation of wood is slow at moderate temperatures and is therefore not the initial driving force inmaterial loss and heat generation in large-scale wood chip storage. [3] When the heat production surpassesthe heat dissipation the reaction will accelerate and eventually result in self-ignition and massive materialloss. Multiple products are produced when wood undergoes thermal degradation. The thermal degradationprocess depends on atmosphere, pressure, temperature, heating rate, time of exposure and moisture content.[11], [4] Examples of products from thermal degradation are char, tar, volatile liquids, carbon monoxide,carbon dioxide, methane, hydrogen and water. Char is a carbon residue. [19]. Thermal analysis of biomassis generally carried out by thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC)at high temperatures. Generally, a TGA scheme of wood shows an endothermic peak around 100◦C whichis the result of evaporation of water. This peak is followed by exothermic degradation processes at elevatedtemperatures. The exothermal peaks are observed in higher temperature intervals during oxygen free anal-ysis. Maryandyshev et al. analyzed spruce with a gas flow rate of 20 · 10−5 m3/min of either air or argon,and a heating rate of 10 ◦C/min. The suggested scheme from this article included three steps: drying,devolatilization and char combustion. Emissions of volatile compounds occur in the devolatilization phase.Drying ended at 92◦C in air and at 120◦C in argon. The devolatilization proceeded between 210-340◦C inair while between 221-377◦C in argon. The char was combusted in air between 347-503◦C. A lower calorificvalue of 18.7 MJ/kg for spruce was determined through DSC. [20] Chemical bonds in wood start to breakabove 100◦C. The thermal degradation between 100-200◦C produces water vapour, non combustible gasesand liquids, such as carbon monoxide, carbon dioxide, some acids and volatile organic compounds. Thethermal degradation of cellulose, hemi cellulose and lignin is slow in this temperature interval. However,the auto-oxidation rate increases. Oxidation is the result of air diffusing and reacting with char. [21] Theeffects of prolonged heat exposure of spruce wood was measured by Fengel in 1966. The temperatures wasraised and kept constant for 24 hours in the interval of 100-200◦C. Weight losses in the magnitude of 0.8wt% began at 120◦C. The weight loss reached 15.5 wt% at 200◦C. [11]

Physical transformation of water

The moisture content of wood has several implications on the degradation outcome and heat generation. Asdiscussed above, fungi and bacteria need moisture to degrade wood but there are also a direct connections toheat production/consumption related to the physical transformation of water. Condensation releases heatwhile evaporation is an endothermic process. [3] Furthermore, the heating value of water is more than twotimes higher than that of dry wood. It therefore takes substantially more energy to cause the same rise intemperature in heavily wet wood than in dry wood. [22]

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Chapter 3 - ModelingThis chapter presents the model developed and tested in this project. Some parameters are explained inthe text, see the nomenclature list for the rest. The chapter starts by going through each sub-model beforecombining these processes and investigating different cases and comparing them to raw data.

3.1 Microbial activity

Microbial degradation of forest residuals (substrate) is an important aspect to consider since it is the initialcause of heat generation and dry matter loss for modeling microbial activity. The substrate was divided intothree fractions. One of these fractions is hard to degrade and hence degrades slowly (SH). One fractionis easy to degrade, this fraction degrades fast in relation to the slow fraction (SE). The third fraction isinert and does not degrade at all (SI). The hard to degrade fraction is composed of cellulose, lignin andhemicellulose while the easily degradable fraction consists of extractives such as smaller sugar units. Theinert fraction is composed of inorganic material. The biological degradation sub model was based on theassumptions listed below. These assumptions are based on the information gathered and displayed in thebackground section of the report.

• Forest residuals of Norway spruce consists of 90% slowly degradable macro molecules, 8% of easilydegradable extractives and 2% of inert inorganic material (dry basis).

• The intial moisture content is 55 wt% (dry basis).

• The extractives are modeld as C6H12O6

• Starting at 15◦C, within a week, the bulk density of extractives are consumed and a considerable amountof wood decaying microorganisms has been formed. The degradation rate slows down but materialkeeps degrading if oxygen is supplied and temperature is controlled. Having optimal temperature,oxygen and moisture for degradation, a magnitude of around 50% is expected to have degraded withinsix months. This degradation percentage is in the magnitude suggested by Erntson et al. [15], [22]

• Heat generation is significant in the initial week, and then slows down just as the material degradation.The heat generation leads to an increase in temperature. Microbial degradation stops at 65◦C.

• Heat generations is related to oxygen consumption and carbon dioxide production. Heat generation ismodeled as aerobic respiration:

C6H12O6 + 6 O2 → 6 CO2 + 6 H2O(l)

∆HR = −1100

[kJ

mol CO2

]• Microorganism colonization and growth can only occur at water contents over 25 wt% (dry basis).

Higher moisture contents does not affect the degradation rate.

• The degradation rate is proportional to oxygen concentration.

• The degradation rate is slow at temperatures below 15◦C and then rapidly increases. It is highest inthe temperature range of 20-30◦C. The rate rapidly decreases at temperatures above 50◦C.

The reaction pathway was based on the work of Ferrero et al. The macro-molecules that are hard to degradeis hydrolyzed into extractives (reaction r1 in figure 3.1). These extractives can both be metabolized bywood-decaying organisms and used to grow new cells (reaction r2 in figure 3.1). The portion of the degraded

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substrate that is used for metabolism gives rise to carbon dioxide, liquid water and heat. The microorganismsalso dies with time (reaction r3 in figure 3.1). This pathway is depicted in figure 3.1 [23]

Figure 3.1: The bio-activity sub-model has been based on the following reaction scheme.

Assuming a closed system uniform in space, the reaction scheme above is translated into the following systemof equations:

ρSH= −r1 (3.1)

ρSE= r1 − r2 (3.2)

ρm = α1r2 − r3 (3.3)

ρd = r3 (3.4)

ρO2= −6α2

MO2

MSE

r2 (3.5)

ρCO2= 6α2

MCO2

MSE

r2 (3.6)

ρ(W,L) = 6α2MH2O

MSE

r2 (3.7)

Here, ρi is the time derivative of the density for specie i, rj denotes the reaction rate of reaction j, Mi is themolar mass of component i and αk expresses the mass-based stoichumetric coefficient of reaction r2, obeyingα1 + α2 = 1. The reaction rate expressions are similar to those proposed by Michaelis-Menten for enzymicreactions.

r1 = − k1ρSH

KS1ρm + ρSH

ρmg1(T )g2(O2)g3(H2O) (3.8)

r2 =k2ρSE

KS2 + ρSE

ρmg1(T )g2(O2)g3(H2O) (3.9)

r3 = k3ρmg1(T )g2(O2)g3(H2O) (3.10)

More specifically, these reactions rates are Monod-kinetic rate expressions which are empirical expressionscommonly used in the field of biological degradation. [23] The rate expressions are further dependent ontemperature, oxygen and moisture. These dependencies are modeled with the functions gi. The temperatureand oxygen dependence was modeled in a similar way to what was described by Ernstson et al. Thedependency functions are all bounded in the interval of [0, 1]. [22]

Table 3.1: Values used when simulating micro-activity. [23]

k1 [s−1] k2 [s−1] k3 [s−1] KS1KS2

[kgm3

]ρm0

[kgm3

]∆HR

[kJkg

][3] α1 α2

4.244 · 10−5 7.094 · 10−5 2.755 · 10−5 52 9.317 · 10−3 3.45 · 10−2 −25000 0.68 0.32

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Figure 3.2: The temperature dependency have been modeled with different functions for different intervalsshown with the different colors.

• The temperature dependence was modeled as the piece-wise linear function, depicted in figure 3.2.

• The oxygen dependence was modeled as the following linear function:

g2(O2) =pO2

pO2,air

(3.11)

Where pO2is the actual partial pressure of oxygen and pO2,air

is the partial pressure of oxygen in air.

• The moisture dependence was modeled as a step function.

g3(H2O) =1, ω(W,L) ≥ 25 wt%

0, ω(W,L) < 25 wt%(3.12)

It is assumed that only processes that produce carbon dioxide and water contribute to heat generation.Accordingly, the heat generation reads as:

STB= 6α2

MCO2

MSE

∆HRr2 (3.13)

Here, STBis the heat source expressed in kJ/(m3 · s). The factor 6 comes from the stoichiometry of the

reaction.

From the mechanism shown in figure 3.1 it can bee seen that all bio-degradation stops if the microorganismsdies since they catalyzes both pathways of degradation. However, in reality the microorganisms will notdie if the conditions in the pile are favorable. A stability and dynamic analysis of this sub-model wasperformed to investigate how the concentration of microorganisms evolves with time. Parameter values usedwhen simulating degradation are shown in table 3.1. Most values were taken from the research presented

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by Ferrero et al. [23] The value of KS1 was adjusted to match the degradation pattern described in theassumptions. This parameter was altered as a response to the analyses previously described. A conclusionfrom the stability analysis were that two conditions must be satisfied to keep the microorganisms alive:

α1k2 > k3, α1k1 > k3 (3.14)

These conditions are met for the parameter values listed in table 3.1. See appendix A for additional infor-mation about how this system was derived.

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3.2 Chemical oxidation

Chemical oxidation is the cause of material loss at elevated temperatures, in which the microorganism dieand microbial activity stops. The chemical oxidation of wood is a complex phenomena at temperatures above200◦C. A lot of the mechanism is yet to be understood. However, the model will focus on a lower temperatureinterval since massive losses occur at temperatures above 200◦C. The model aims to predict how to avoidgetting such high temperatures in the pile. The chemical oxidation reaction was simplified to completecombustion. This case generates most low energy density gaseous products which hinders transport whilegenerating the maximum amount of heat leading to maximum heat accumulation and threats of runawayphenomena. It can therefore be consider to be the worst case. The chemical oxidation sub model was basedon the assumptions listed below. These assumptions are based on information presented in the introduction.

• The chemical oxidation is negligible at low temperatures and slow between 80-100◦C. Prolonged expo-sure at 120◦C results in degradation.

• The weight loss during the first 24 hours is very low at a constant temperatures of 120◦C.

• The weight loss during the first 24 hours reaches a magnitude of 15-20 wt% at a constant temperatureof 200◦C.

• The oxidation products are carbon dioxide and water.

• The substrate degradation is of first order with respect to the substrate.

• The reaction rate depends on the temperature and the partial pressure of oxygen.

• The heat production is modeled with the lower calorific value of 18.7 [MJ/kg].

Table 3.2: Parameters used to simulate chemical oxidation.

ν1 ν2 ν3 k0 [s−1] [23] EA/R [K] [23] ∆HC

[MJkg

][20]

1.0565 1 0.67795 8.15 · 105 12, 509 −18.7

The substrate composition has been decided based on the chemical composition data for GROT presentedin Branslehandboken 2012 . The composition on moisture and ash free basis is 53.1 wt% C, 6 wt% H, 40wt% O, 0.04 wt% S, 0.31 wt% N and 0.02 wt% Cl. [6] Weight fractions is converted to molar fractions byequation 3.15.

xi =ωi

Mi∑ ωj

Mj

(3.15)

Ignoring S, N and Cl, the composition on the normalized form thus reads as:

C1HYOZ

Y = 1.3559

Z = 0.5650

(3.16)

The following reaction pathway have been used to simulate oxidation.

C1HYOZ + ν1 O2 → ν2 CO2 + ν3 H2O (3.17)

The density source terms and heat generation was modeled as a first order kinetic reaction with respect tothe substrate. This approach have been applied in many studies. [24], [23], [25] The degradation is alsoproportional to the oxygen concentration.

ρS = r4 = −(ρSH+ ρSE

)k0e(−EA/(RT ))g2(O2) (3.18)

Where k0 is the pre-exponential factor, EA is the activation energy, R is the gas constant, the oxygendependency is shown in equation 3.11.

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Assuming a spatially uniformed closed system, the following equations describes degradation and heat gen-erated by chemical oxidation.

ρSH= − ρSH

ρSH+ ρSE

r4 (3.19)

ρSE= − ρSE

ρSH+ ρSE

r4 (3.20)

ρj = −νjMj

MSr4 (3.21)

STC= ∆HCr4 (3.22)

Here, STCis the heat source expressed in kJ/(m3 · s), ∆HC is the heat of combustion and νj denotes the

stoichiometric coefficient of substance j. Stoichiometric coefficients are negative for reactants and positivefor product species. See appendix B for additional information for how the system was derived.

3.3 Physical transformation

Condensation and evaporation of water was treated by considering saturated atmosphere with respect towater vapor inside the porous media. The pressure/density of water vapor then becomes a function oftemperature. The change in water vapor therefore has to be coupled with the temperature evolution withtime which is gained from the energy balance of the system. This is shown below in equation 3.23. Theassumption that the system is saturated provides a convenent modelling framework that also was adoptedin earlier works [15]. See appendix C for an evaluation of the physical transformation sub-model.

ρ(W,V ) =dT

dt

dρ(W,V )

dT(3.23)

The vapor pressure may be related to the temperature inside the stack through an emperical expressioncalled Antoine’s law.

log p(W,V ) = A− B

T + C(3.24)

Here, A, B and C are substance specific constants expressed. Combining Antoine’s law with the ideal gaslaw allows the density to be expressed as a function of temperature.

ρW,V (T ) = exp

(A− B

T + C

)MH2O

RTfε (3.25)

Where f is a conversion factor and ε expresses the porosity of the bed. The temperature derivative ofequation 3.25 is given below:

dρ(W,V )

dT= fε

Mv

RTexp

(A− B

T + C

)(B

(C + T )2− 1

T

)(3.26)

Parameter values used in equation 3.26 are listed in table 3.3

Table 3.3: Parameter values used to describe physical transformation. Antoine’s constants are adjusted fornatural logarithm and Kelvin.

A [26] B [26] C [26] ε f[

kgPagmmHg

]18.669 403.02 −38.15 0.5 10−3 · 133.32

10

3.4 Transport

Transport of species may be caused by different phenomena such at diffusion, natural convection, buoyancyforces or external flows. Wind could be modeled as an external flow in which addition of oxygen and nitrogeninto the pile is added. Diffusion is caused by random motions of molecules and is expressed by fick’s law,see equation 3.27. [27]

NA1= −DA∇CA

[kg

m2s

](3.27)

Transport caused by natural convection and buoyancy forces in a pile is an effect of the temperature increaseinside the stack. The increasing temperature leads to an increase in pressure which creates natural convection.Natural convection caused by a pressure increase in porous media is controlled by Darcy’s Law, which isshown below in spacial direction i for a laminar flow. [28]

NA2 = −ρAβ

µli∆p

[ms

](3.28)

Buoyancy forces act on densities which becomes lower at elevated temperatures. This means that a coherentmovement of gaseous species in an upwards direction within the pile is initiated. The hot gases are replacedby colder gases. Buoyancy effects are expressed equation 3.29. [29]

NA3 = g∆ρA

[kg

m2s

](3.29)

Ferrero et al. considered transport by diffusion and convection. Convection was considered by increasingdiffusion coefficients. Diffusion is caused by random movements of molecules, here the flux is driven bya concentration gradient. [23] Ernstson et al. investigated the importance of convection by studying theRayleigh number. The Rayleigh number can be expressed on an energy basis as well as on a mass basis. Thisnumber shows the ratio of heat transferred by free convection and conduction or the ratio of mass transferredby natural convection and diffusivity. Ernstson et al. concluded that natural convection is important whendescribing transfer in a wood pile. [22]

The interplay between these transport mechanisms needs further investigations through literature beforebeing implemented into the model. In the following section energy and mass balances have been setup for asmall homogeneous volume element. These balances include a transport term but only isolated cases wereperformed to evaluate the model. The following section develops this modelling approach further.

3.5 All processes

All processes were lastly combined and examined together to get an understanding for how these processesinteract with each other. Consider the volume element shown in figure 3.3. If a small volume is consider thesystem can be treated as homogeneous. Conditions may then be changed to consider different placementsinside the pile.

3.6 The general case

The mass balances over the system are described below, these are mostly based on the sub-models whichare previously described in the report. An additional transport term was added to these balances. The massbalances includes biochemical reactions (green), chemical oxidation reactions (red), physical transformationof water (blue) as well as transport (black).

ρSH= −r1 −

ρSH

ρSH+ ρSE

r4 (3.30)

11

ρSE= r1 − r2 −

ρSE

ρSH+ ρSE

r4 (3.31)

ρSI= 0 (3.32)

ρm = α1r2 − r3 (3.33)

ρd = r3 (3.34)

ρ(W,V ) =dT

dtfεMv

RTexp

(A− B

T + C

)(B

(C + T )2− 1

T

)(3.35)

ρO2= −6α2

MO2

MSE

r2 − ν1MO2

MSr4 −

FO2

V(3.36)

ρCO2 = 6α2MCO2

MSE

r2 + ν2MCO2

MSr4 −

FCO2

V(3.37)

ρ(W,L) = −ρ(W,V ) + 6α2MH2O

MSE

r2 + ν3MH2O

MSr4 −

FW,VV

(3.38)

ρN2 = −FN2

V(3.39)

The energy balance that describes the temperature evolution is shown in equation 3.40.

T =Q− F(W,V )

V ∆HV ap − 6α2MCO2

MSE∆HRr2 −∆HCr4∑

ρicp,i +dρ(W,V )

dT ∆HV ap

(3.40)

Where, Q represents the heat transfer with the surroundings, −F(W,V )

V ∆HV ap is the heat that leaves the

system through water transport, −6α2MCO2

MSE∆HRr2 and −∆HCr4 are the heat generating terms from the

bio chemical and chemical reactions, respectively. The denominator shows that heat are used to heat up thesystem as well as to evaporate water. It is important to note that the specific heat capacity of the substratedepends on its moisture level. This relationship is expressed in equation 3.41.

cp,s =cp,(W,L)ω(W,L) + cp,DM

ω(W,L) + 1(3.41)

Initial conditions

The initial concentrations of gaseous species are dependent on the initial temperature and pressure of thesystem. The pressure is initially built up by water vapor, oxygen and nitrogen. The numbers presented herecorresponds to an initial pressure of 1 atm and a starting temperature of 15◦C. The atmosphere is saturatedwith water vapor. The solid is assumed to be porous material with an apparent density of 410 kg/m3,comprised of 90 wt% hard to degrade substrate, 8 wt% easy to degrade substrate and 2 wt% inert inorganicmaterial. All concentrations have the unit kg/m3.

Gaseous species : ρ(W,V )0 = 0.0064, ρO20= 0.1397, ρCO20

= 0, ρN20= 0.4598,

Liquid species : ρ(W,L)0 = 225.5,

Solid species : ρSH0= 369, ρSE0

= 32.8, ρSI0= 8.2, ρm0

= 3.45 · 10−2, ρd0 = 0

(3.42)

12

Cases

Two cases were run to evaluate the model. The first case looks at an insulated system, meaning that noheat or mass is exchanged with its surroundings. Here the initial oxygen concentration is equal to that inair. The second case is an insulated system with an endless depot of oxygen. The two cases were run to seehow the system behaves at these two extremes. These two cases are purely theoretical and are only set up toinvestigate the model. The second case could be consider a worst case scenario since all heat is accumulatedwithin the system, while the unlimited supply of oxygen keeps the degradation processes going.

Figure 3.3: The system is a homogeneous volume element.

3.6.1 Case 1 - ’Deep inside the stack’ (No boundary effects)

The system becomes a insulated system if no boundary effects are considered since all neighbouring elementshave the same temperature and pressure evolution, eliminating all driving forces for transport. The massand energy balances were therefore transferred into the system presented here.

ρSH= −r1 −

ρSH

ρSH+ ρSE

r4 (3.43)

ρSE= r1 − r2 −

ρSE

ρSH+ ρSE

r4 (3.44)

ρSI= 0 (3.45)

ρm = α1r2 − r3 (3.46)

ρd = r3 (3.47)

ρW,V =dT

dtfεMv

RTexp

(A− B

T + C

)(B

(C + T )2− 1

T

)(3.48)

ρO2 = −6α2MO2

MSE

r2 − ν1MO2

MSr4 (3.49)

ρCO2= 6α2

MCO2

MSE

r2 + ν2MCO2

MSr4 (3.50)

ρW,L = −ρW,V + 6α2MH2O

MSE

r2 + ν3MH2O

MSr4 (3.51)

ρN2= 0 (3.52)

T =−6α2

MCO2

MSE∆HRr2 −∆HCr4∑

ρicp,i +dρW,V

dT ∆HV ap

(3.53)

13

3.6.2 Case 2 - ’Endless depot of oxygen’ (Constant optimal oxygen concentra-tion)

This case studies how the model behaves if there is an unlimited amount of oxygen in the insulated system.This yields in the same energy and mass balances as in case 1, although here the function g2(O2) is alwaysset to 1 to mimic an unlimited supply of oxygen.

14

Chapter 4 - Results and discussionThis section presents results from the simulations from case 1 and 2. Five different initial temperatures havebeen simulated. The five chosen initial temperatures were 5, 10, 15, 20 and 35◦C since these temperaturestarts at different biochemical reaction rates and catches a wide range of possible outdoor temperatures.

4.1 Case 1

The first case looked at an isolated system with an initial oxygen concentration equal to that in air atdifferent initial temperatures. Temperature profiles, oxygen consumption, absolute and percentage baseddry matter degradation during and after 60 days of storage are illustrated for this case.

Figure 4.1 shows the temperature profiles for the five different initial temperatures. A slight temperatureincrease is visible in all cases before the temperature relaxes to a steady-state. Steady-state is reachedfastest at an initial temperature of 20◦C. At 20◦C steady state is reached after approximately 2 days. Thetransmission towards steady sate is slowest at 5◦C where it is reached around 25 days. Steady-state occursafter 5 days of storage at 15◦C.

Figure 4.2 shows the oxygen consumption over time in the system. Here it can be seen that the oxygenconsumption is slower at lower initial temperatures. The slightly higher initial concentration at lower tem-peratures are understood after looking at the ideal gas law. The ideal gas law determines that the numberof moles increases with decreasing temperatures if the pressure and volume stays constant.

Figure 4.3 shows the absolute substrate degradation of the system. The figure illustrates that only a smallamount of the wood degrades by consuming the initial oxygen available in the system. More wood degradesat lower temperatures. The degradation is slower at lower temperatures.

Figure 4.4 shows the degraded percentage after 60 days of storage. A very small amount has degraded.Slightly higher degrdation is seen at lower initial temperatures.

The results from the simulations of the closed system are to be expected. The temperature starts to increasewithin the first week at an initial temperature of 15◦C which is the expected outcome from the micro-activity in the stack. The pattern of increasing time to reach the final temperature state with decreasinginitial temperatures below 20◦C is caused by slower reaction rates. This also explains why it takes slightlylonger to reach the final temperature state when starting at 35◦C compared to 20◦C. The higher degradationat lower initial temperatures is caused by the increase in initial oxygen concentration. There is more oxygenin the system at lower temperatures. The low total degradation and temperature increase voice that thisscenario is far off from the situation occurring in a real biomass stack. However, the importance of includingoxygen transport is thoroughly shown by studying this case.

15

Figure 4.1: Temperature evolution in the isolated system for different initial temperatures. The dashed lineshows the critical temperature at which biological activity comes to a rest.

Figure 4.2: Oxygen consumption in the isolated system for different initial temperatures.

16

Figure 4.3: Substrate degradation in the isolated system for different initial temperatures.

Figure 4.4: Percentage of degradation in the isolated system as a function of the initial temperature.

17

4.2 Case 2

Case 2 investigated an isolated adiabatic system with an endless depot of oxygen, meaning that the oxygendependence function g2(O2) always equaled 1. Here the temperature evolution, absolute and percentagebased degradation are shown for the five initial temperatures. Also displayed here are temperature andhumidity evolutions for different initial concentrations of liquid water in the substrate. In these two graphsthe initial temperature was set to 15◦C. The numerical simulation was stopped at or just before thermalrunaway.

Figure 4.5 shows the temperature evolution for the five investigated initial temperatures. The temperatureevolves fast until the cut of temperature for microbial activity is reached. Thereafter follows a time ofapparent linear evolution which itself is followed by thermal runaway. The apparent linear evolution isexpected since the chemical oxidation reaction rate behaves in this manner at constant temperatures.

Figure 4.6 shows temperature profiles for different initial liquid water concentrations at an initial temper-ature of 15◦C. This figure shows that thermal runaway is reached faster for lower initial weight fractions ofliquid water. The reason for this is the lower heat capacity of the wet solid matrix.

Figure 4.7 shows the weight fraction of liquid water versus time. The weight fraction of liquid waterstays close to constant until thermal runaway is reached. The wood does not dry out in this case beforethermal runaway happens since no water is allowed to leave the system. The slight increase is observed sincemore liquid water is produced in the bio-chemical and chemical reactions than is evaporated to keep thetemperature saturated. This stays true until thermal runaway occurs.

Figure 4.8 shows the absolute substrate degradation over time. A fast initial degradation is followed bya period of slower degradation before degradation starts to accelerate again. The fast initial degradation iscontrolled by microbial activity while the slow degradation in the second stage of the process is controlledby the chemical oxidation reaction.

Figure 4.9 shows the percentage of degraded biomass just before thermal runaway is reached. The degra-dation percentage varies between 1.5-2.3%. The reason that the degradation is slightly higher for the lowerinitial temperatures is that the degradation caused by bio-activity proceeds over a larger temperature range.

Figure 4.10 shows how much of the degraded material that was consumed in microbial processes. Here thedegradation percentage varies between 0.9 to 1.85%.

Case 2 has optimal conditions for heat accumulation since no heat is transferred to the surroundings whileoxygen is always kept at an optimal level for degradation. This case is therefore interesting to look at wheninvestigating how the model predicts thermal runaway. Two important factors to take into account are heataccumulation and how much energy is needed to heat up the system by 1◦C. Different weight fractions ofwater have been looked at to see how long it takes to reach thermal runaway depending on how much liquidwater the substrate contains. Starting with a lower initial weight fraction of liquid water than the fibersaturation point (0.25) would prevent microorganism activity which is not interesting to investigate. Thefastest thermal runaway occurs after 150 days of storage, which is a much longer time than what is foundin the the field study. The model fails to catch the possibility of fast temperature increases all the way upto over 100◦C which is observed in some stacks. Some accuracy could be lost due to the fact that the woodis not allowed to get drier after the bio-chemical reaction have reached its cut off temperature. It shouldhowever be noted that Stockholm Exergi uses a flue gas condenser which allows the moisture content tobe as high as 40%. There is therefore no need to dry the fuel too much before consuming it. The datafrom the field study also shows a moisture content above 25 wt% at all times. Another important takeaway from this simulation is that the final degradation percentage from figure 4.9 is around 2.3% while thedegradation from the biological processes shown in figure 4.10 are around 1.85%. The degradation is veryslow in the temperature range between 65-80◦C before chemical oxidation starts to accelerate. The very

18

slow heat generation in this temperature interval indicates that the model might not predict runaway if heattransfer with the surrounding is added. The temperature range between 65-80◦C is therefore considered anarea of improvement and need more investigation. This case shows that the microbial processes and chemicaloxidation reactions in the model have low interaction with each other. These processes controls materialloss in different temperature ranges which is in agreement with literature. However, the gap between theseprocesses must be adjusted to match reality. This case does not reveal the whole truth about how the processof physical transformation interacts with the other processes. To determine this transport of water must beincluded.

Figure 4.5: Temperature evolution in the adiabatic system for different initial temperatures.

19

Figure 4.6: Temperature evolution in the adiabatic system for different initial moisture levels.

Figure 4.7: Time evolution of moisture level for the adiabatic system for different initial moisture levels inthe substrate.

20

Figure 4.8: Substrate degradation in the adiabatic system for different initial temperatures.

Figure 4.9: Degradation percentage in the adiabatic system for different initial temperatures.

21

Figure 4.10: Percentage degraded by biological processes in the adiabatic system for different initial temper-atures.

22

Chapter 5 - Future workSLU togheter with Stockholm Exergi and other partners has an ongoing field study project in progress aboutbiomass degradation. Among other quantities, temperature and gas emissions will be measured. Thesemeasurements will be going on in 2019-2020 at different locations in Sweden. It appears beneficial thatboth temperatures and emissions are being measured simultaneously since it makes it possible to correlateemissions to the different processes. The gases that I would suggest to measure in order to better understandmass loss and substrate degradation are carbon dioxide, carbon monoxide, methane and oxygen. Measuringthe oxygen concentration in the stack will give information about how important anaerobic processes are toconsider. Measuring gaseous concentrations could also provide information about how gases are transportedinside the stack. Further research in literature is needed before adding transport to the model. To be able toasses the environmental impact of biomass storage emissions of sulfur oxide, hydrogen sulfide and laughinggas should also be measured.

Two approaches are suggested to increase the precision in the temperature interval between 65-80◦C. Thefirst approach would be to learn more about the biology in this temperature range. May the heat generationand material degradation be caused by thermophilic bacteria? Does the microorganisms die off with timeonce 65◦C is reached? Here it could be a good idea to include a biochemist.

The second approach would be to perform long exposure oxidation experiments at constant temperature in acontrolled lab environment. Equipment needed are a TGA-analysis which is to be coupled with a gas emissiondetector. Experiments should be performed at 80◦C under both nitrogen and oxygen atmospheres and goon for at least a week. These measurements would yield information about how degradation depends on thepartial pressure of oxygen and which products are formed during different atmospheres. Also detectable ifany, degradation rate changes due to mechanical changes in the wood caused by low temperature oxidation.However, here there are some challenges that need to be considered. Chemical oxidation in low temperaturesis slow, therefore it may be hard to detect emissions. One solution could be to perform these experimentsin a closed system in which the gases would accumulate.

23

Chapter 6 - ConclusionsAerobic processes in the pile consumes oxygen to degrade dry matter and produce heat. The initial oxygenconcentration in air trapped in the stack is too low to facilitate significant losses and heat generation.Oxygen transport into the stack is thus vital to predict storage behaviour. Biological processes are knownto control dry matter degradation at temperatures below 65◦C while chemical oxidation reactions controlthe losses at elevated temperatures above 80◦C which is captured by the model. However, the model fails toaccurately capture the interplay between these processes in the temperature range between 65-80◦C, leadingto inaccurate predictions of thermal runaway and dry matter losses.The temperature reaches 65◦C in an isolated adiabatic system with an unlimited supply of oxygen within 2to 20 days, depending on the initial temperature. The degradation of biomass within this time window isbetween 1.0-1.8%. This is significantly lower than the dry matter losses observed in the stacks in the field.The deviation is explained by heat transfer to the environment which keeps the temperature below 65◦C fora longer time which allows the microorganisms to degrade more wood.

24

Chapter 7 - Appendices

7.1 Appendix A - Biological degradation

Evaluation of the biodegradation sub model.

7.1.1 Dry matter degradation

Ferrero et al. [23] created a modeled which considered an easily degradable fraction (SE) and a slowlydegradable fraction (SH) and such a model was examined within this thesis. The model assumes that boththe hard and easy fractions are consumed by microorganisms (m). The substances that are hard to degradeis through enzyme reactions turned into easy degradable substances. The extractives are partly consumedto grow new microorganisms and partly oxidized through metabolism. The degradation of solid materialtherefore occurs according to the system below:

ρSH= −r1 (7.1)

ρSE= r1 − r2 (7.2)

ρm = α1r2 − r3 (7.3)

r1 = − k1ρSH

KS1ρm + ρSH

ρm (7.4)

r2 =k2ρSE

KS2+ ρSE

ρm (7.5)

r3 = k3ρm (7.6)

Where ri denotes reaction rate and α1 represents the mass fraction that is used to grow new microorganisms.The reaction rates r1 and r2 are based on Monod-kinetics which are a widely used within the framework ofbio degradation. Table 7.1 shows a sample of paramters from Ferrero et al. [23]

Table 7.1: A sample of parameters from Ferrero et al. [23]

k1 [s−1] k2 [s−1] k3 [s−1] KS1KS2

[kgm3

]ρm0

[kgm3

]4.244 · 10−5 7.094 · 10−5 2.755 · 10−5 6.5 9.317 · 10−3 3.45 · 10−2

Stability analysis

It is reasonable to assume that the degradation in equation 7.1 is slower than the degradation in equation7.2. Hence, Investigations of the initial fast process governed by equations 7.2 and 7.3 was made by assumingthe hard degradable fraction to be constant. The quasi-steady state (QSS) of the remaining two equationscould readily be studied. Setting equation 7.2 and 7.3 to zero and solving for the densities of microorganismsand easily degradable substances yields in the following expressions:

ρm =1

KS1

(−ρSH

+k1ρSH

(KS2+ ρSE

)

k2ρSE

)(7.7)

ρSE=

k3KS2

α1k2 − k3(7.8)

25

Equation 7.7 gives quasi-steady-state values for the easy degradable fraction while equation 7.8 gives thequasi-steady-state value for the microorganisms. The intersection of the two functions determines the possibleQSS states of the system. The QSS value of the microorganisms is obtained by substituting equation 7.8into equation 7.8 resulting in the following point:

ρ0SE=

k3KS2

α1k2 − k3, ρ0m =

ρSH(α1k1 − k3)

k3KS1

(7.9)

Here it can be observed that the fast process have a quasi-steady sate in the first quadrant of the phaseplane depicted in figure 7.1 if the following two conditions are satisfied:

α1k2 > k3, α1k1 > k3 (7.10)

To ensure that these conditions are satisfied α1 was taken as 0.68 which is the biomass yield coefficientreported by Ferrero et al. [23]. The stability of the reduced fast system was analyzed by studying how thesystem behaves when deviated QSS. This was done both qualitatively and by linearizing the system at theQSS point. Figure 7.1 shows the phase plane of the fast system given by equations 7.2 and 7.3. Figure 7.1qualitatively shows how the system operates when deviated from the QSS point.

Figure 7.1: The arrows qualitatively show points trajectory in the plane.

Linearizing the system around the QSS gives information about the eigenvalues of the system which deter-mines stability. For performing this analysis, let us rewrite the fast system given by equations 7.2 and 7.3as:

ρSE= f(ρSE

, ρm) (7.11)

ρm = g(ρSE, ρm) (7.12)

26

Moving away from the steady-state.

ρSE= ρ0SE

+ ∆ρSE(7.13)

ρm = ρ0m + ∆ρm (7.14)

Taking the derivative of 7.13 and 7.14.

ρSE=

d

dt(ρ0SE

+ ∆ρSE) = ∆ρSE

(7.15)

ρm =d

dt(ρ0m + ∆ρm) = ∆ρm (7.16)

Applying Taylor expansions.

∆ρSE= f(ρ0SE

+ ∆ρSE, ρ0m + ∆ρm)

≈ f(ρ0SE, ρ0m) + fρSE

(ρ0SE, ρ0m)∆ρSE

+ fρm(ρ0SE, ρ0m)∆ρm

(7.17)

∆ρm = g(ρ0SE+ ∆ρSE

, ρ0m + ∆ρm)

≈ g(ρ0SE, ρ0m) + gρSE

(ρ0SE, ρ0m)∆ρSE

+ gρm(ρ0SE, ρ0m)∆ρm

(7.18)

This results in the following linearized system:

∆ρSE= fρSE

(ρ0SE, ρ0m)∆ρSE

+ fρm(ρ0SE, ρ0m)∆ρm (7.19)

∆ρm = gρSE(ρ0SE

, ρ0m)∆ρSE+ gρm(ρ0SE

, ρ0m)∆ρm (7.20)

Taking the deriviatives of 7.2-7.3.

∆ρSE=

(k2ρ

0SEρ0m

(KS2− ρ0SE

)2− k2ρ

0m

KS2+ ρ0SE

)∆ρSE

+

(k1ρSH

Ks1ρ0m + ρSH

− k1ρSHKS1ρ

0m

(Ks1ρ0m + ρSH

)2−

k2ρ0SE

KS2+ ρ0SE

)∆ρm

(7.21)

∆ρm =

(α1k2ρ

0m

KS2 + ρ0SE

−α1k2ρ

0SEρ0m

(KS2 + ρ0SE)2

)∆ρSE

+

(α1k2ρ

0SE

KS2 + ρ0SE

− k3)

∆ρm (7.22)

Plugging in the values from table 7.1 gives:

∆ρSE= −31 · 10−3∆ρSE

− 1.5685 · 10−6∆ρm (7.23)

∆ρm = 21 · 10−3∆ρSE+ 0 ·∆ρm (7.24)

A stable steady-state has negative eigenvalues, the system is therefore expected to converge towards steady-state through 7.23. This was shown numerically in figure 7.2.

27

Figure 7.2: The figure illustrates how the reduced system with a constant value of the slowly degradablefraction approaches quasi-steady state. The blue star show the initial value, the pink curve shows thetrajectory and the green star shows the final value.

Dynamics

It’s of interest to know how the reaction rates r1 and r2 behaves. This is illustrated in figures 7.3-7.4. Thesefigures show that the reaction rates may be simplified to k1ρm and k2ρm when ρSE

and ρSHare not to close

to zero, which is the initial case. These simplifications leads to the following system:

ρSH= −k1ρm (7.25)

ρSE= k1ρm − k2ρm (7.26)

ρm = α1k2ρm − k3ρm (7.27)

which has the following analytic solutions with the initial conditions ρSH(0) = ρSH0

, ρSE(0) = ρSE0

, ρm(0) =ρm0.

ρSH= ρSH0

− −k1α1k2 − k3

ρm0(e(α1k2−k3)t − 1) (7.28)

ρSE= ρSE0

+k2 − k3α1k2 − k3

ρm0(e(α1k2−k3)t − 1) (7.29)

ρm = ρm0e(α1k2−k3)t (7.30)

As, mentioned this simplified system is only valid before the easy fraction is heavily consumed. These analyticsolutions show that the duration of the fast process depends on the initial condition of microorganisms which

28

is to be expected. The full time dependent system was thereafter integrated numerically. Solutions are shownin figure 7.5 and figure 7.6

Figure 7.3: Reaction rate r1 at different concentrations of microorganisms

Figure 7.4: Reaction rate r2 at different concentrations of microorganisms

29

Figure 7.5: Substrate degradation obtained from numerical integration of equations 7.1-7.3. Initial conditionsare ρSH

= 369 [kg/m3] and ρSE= 32.8 [kg/m3] and ρm = 3.45 · 10−2 [kg/m3]

30

Figure 7.6: Reprint of the data from figure 7.5 highlighting the first week.

31

Figure 7.7: Total substrate degradation profiles obtained from the integration of equations 7.1-7.3 for differentinitial microorganism concentrations. Initial conditions are ρSH

= 369 [kg/m3] and ρSE= 32.8 [kg/m3].

Figure 7.8: Total substrate degradation profiles obtained from the integration of equations 7.1-7.3 for varyingvalues of KS1

. Initial conditions are ρSH= 369 [kg/m3] and ρSE

= 32.8 [kg/m3] and ρm = 3.45·10−2 [kg/m3]

32

Figures 7.5 and 7.6 show that the degradation follows the expected route. An initial time scale where boththe easily degradable substance and the hard to degrade substance are consumed followed by a degradationperiod solely controlled by the slow fraction. However, the density evolution does not completely matchwhat is expected from literature. It can be concluded by studying the quasi-steady state point shownin expression 7.9 and the analytic solutions in equations 7.28-7.30 that the parameter KS1

and the initialcondition of microorganisms are suitable parameters to change to adjust the model. The initial concentrationof microorganisms controls the fast process, while KS1 controls the slow evolution. Figure 7.7 showcases howthe initial degradation changes depending on the initial condition of microorganisms. Figure 7.8 illustrateshow the second timescale changes with changing values of KS1

.

7.1.2 Heat generation

The temperature evolution is governed by oxygen transport which makes it tricky to evaluate the heatgeneration without adding transport equations. An evaluation of the heat generation was done by consideringthe heat generated in a isolated system with an initial concentration of oxygen corresponding to the value inair. The density of the dry matter and the moisture content was kept constant during this estimation. Theoxygen concentration in air, modeled as an ideal gas at normal temperature and pressure, is 8.73 mol O2/m

3

on dry air basis. The temperature increase resulting from microbial activity is expressed in equation 7.31.Table 7.2 shows parameter values used to calculate heat generation.

∆T = −∆HC

ρcpnCO2

(7.31)

Table 7.2: Values used to evaluate heat generation by microbial activity.

∆HC

[kJ

mol CO2

][3] CpDM

[kJkgK

][22] CpW

[kJkgK

]ρDM

[kgm3

][22] ρ (ω(W,L) = 0.55)

[kgm3

]1100 1.3 4.18 410 635.5

The heat capacity is expressed by equation 7.32.

cp =Cp(W,L)

ω(W,L) + CpDM

(1 + ω(W,L))(7.32)

Where ω(W,L) is the weight fraction of water on dry basis. It is apparent from the values displayed in table7.2 that the moisture content within the substrate affects the heating rate. A moisture content of 55 wt%yields in a temperature increase of 4.81 K while the temperature increase is 18.02 K for dry wood.

33

7.2 Appendix B - Chemical oxidation

Evaluation of the chemical oxidation sub model.

7.2.1 Material degradation

The substrate degradation by chemical oxidation was modeled as a first order reaction with respect to thedegradable fractions of the substrate concentration:

ρS = −(ρSH+ ρSE

)k0e(−EA/(RT ))g2(O2) (7.33)

The analytic solution to equation 7.33 is expressed below.

ρS(t) = (ρSH+ ρSE

)0e−βt (7.34)

β = k0e(−EA/(RT ))g2(O2) (7.35)

Where ρS = ρSH+ ρSE

Table 7.3: Kinetic parameters from Ferrero et al. [23]

k0 [s−1] EA/R [K]8.15 · 105 12.509

Table 7.3 shows kinetic oxidation parameters used by Ferrero et al. [23] These parameters have been usedin equation 7.34 to produce figure 7.9. Figure 7.9 shows solutions at constant temperatuares of 120◦C and200◦C.

Figure 7.9: Degradation by chemical oxidation at constant temperature.

34

Figure 7.9 shows that the degradation by chemical oxidation during 24 hours, with parameter values formFerrero et al. [23], is in the accepted magnitude.

35

7.3 Appendix C - Physical transformation

The physical transformation was approached by assuming that the atmosphere inside the stack is saturatedwith water vapor. Assuming saturated vapor means that the vapor pressure is a function of temperature.In this work the empirical function shown below has been used to calculate the saturation pressure.

log p(W,V ) = A− B

T + C(7.36)

This function was tested against tabulated data from Tabeller och diagram for energitekniska berakningar[30]. The result is shown in figure 7.10.

Figure 7.10: Vapor pressure versus temperature both calculated values and tabulated values are shown.

Once the saturation pressure is given, the density of water vapor may be expressed by the ideal gas law.

ρ(W,V )(T ) = exp

(A− B

T + C

)MH2O

RTfε (7.37)

Here, f is an conversion factor that converts the pressure to Pa and weight to kg while ε describes theporosity of the pile. It is of interest to see in which magnitude the vapor density is at in the temperaturerange between 0-100◦C since the model assumes saturated water vapor. If the values of vapor density arerelative low compared to the initial concentration of liquid water the assumption holds for a large temperaturerange. The density evolution with temperature is shown in figure 7.11

36

Figure 7.11: Density of water vapor at saturated conditions.

Figure 7.11 shows that the saturation density is well below the 225.5 kg/m3 which is the initial condition ofliquid water inside the stack. This indicates that the model may hold for a long time. Transport phenomenamust be included to determine how long it takes before the stack is dried out.

37

7.4 Appendix D - All processes

This appendix accounts for the derivation of the temperature evolution with time. See the previous ap-pendixes for information about reaction rates etc.

7.4.1 Energy balance

Figure 7.12: Caption

Let us consider a homogeneous domain with volume V . Starting from the mass balances which includesbiochemical reactions (green), chemical oxidation reactions (red), physical transformation of water (blue) aswell as transport (black). Transport is only considered for gaseous species.

ρSH= −r1 −

ρSH

ρSH+ ρSE

r4 (7.38)

ρSE= r1 − r2 −

ρSE

ρSH+ ρSE

r4 (7.39)

ρSI= 0 (7.40)

ρm = α1r2 − r3 (7.41)

ρd = r3 (7.42)

ρ(W,V ) =dT

dt

dρ(W,V )

dT(7.43)

ρO2= −6α2

MO2

MSE

r2 − ν1MO2

MSr4 −

FO2

V(7.44)

ρCO2 = 6α2MCO2

MSE

r2 + ν2MCO2

MSr4 −

FCO2

V(7.45)

ρ(W,L) = −ρ(W,V ) + 6α2MH2O

MSE

r2 + ν3MH2O

MSr4 −

FW,VV

(7.46)

ρN2 = −FN2

V(7.47)

Where Fj refers to the mass flow out of the domain in kg/s. Here, j = O2, N2, CO2 and water vapor.

38

The energy of the system may be expressed as:

H =∑

ρihi

[kJ

m3

](7.48)

The time evolution becomes

dH

dt=

d

dt

(∑ρihi

)=

(dρidthi + ρj

dhjdt

)+ ...+

(dρidthn + ρn

dhndt

)(7.49)

Which is equal to the energy that is transferred with the system and its surroundings.

dH

dt= Q−

FN2hN2 + FO2hO2 + FCO2hCO2 + F(W,V )h(W,V )

V(7.50)

Where Q is the heat flow per unit volume into the domain.

The second term in equation 7.49 was treated in the following fashion:

dhidt

=dhidT

dT

dt= cp,i

dT

dt(7.51)

Combining the mass balances with equations 7.49 to 7.51 yields in the following expression:

Q−FN2

hN2+ FO2

hO2+ FCO2

hCO2+ F(W,V )h(W,V )

V= r1(hSE

− hSH)

+ r2

(6α2

MH2O

MSE

h(W,L) + 6α2MCO2

MSE

hCO2 − 6α2MO2

MSE

hO2 − hSE+ α1hm

)+ r3(hd − hm)

+ r4

(−ν1

MO2

MShO2

+ ν2MCO2

MShCO2

+ ν3MH2O

MSh(W,L) −

ρSH

ρSH+ ρSE

hSH− ρSH

ρSE+ ρSE

hSE

)−FN2

hN2+ FO2

hO2+ FCO2

hCO2+ F(W,V )h(W,L)

V+∑

Cp,iρidT

dt+dT

dt

dρW,VdT

∆HV ap

(7.52)

Rearranging for temperature and assuming that the energy transformation is neglectable when the hardfraction is turned into the easy fraction as well as when the active microorganism dies results in the finalexpression shown below:

T =Q− F(W,V )

V ∆HV ap − 6α2MCO2

MSE∆HRr2 −∆HCr4∑

ρicp,i +dρ(W,V )

dT ∆HV ap

Where

− 6α2MCO2

MSE

∆HR = 6α2MH2O

MSE

h(W,L) + 6α2MCO2

MSE

hCO2 − 6α2MO2

MSE

hO2 − hSE+ α1hm

−∆HC = −ν1MO2

MShO2

+ ν2MCO2

MShCO2

+ ν3MH2O

MSh(W,L) −

ρSH

ρSH+ ρSE

hSH− ρSH

ρSE+ ρSE

hSE

(7.53)

7.5 Case 2

The energy that is required to heat a system is decided by the amount of mass and the heating values of theindividual materials. In the second case an endless depot of oxygen is simulated by asserting the value 1 tothe dependency function g2(O2) at all times while keeping the initial value of oxygen to that in air. Thispresents a inaccuracy since the models built up carbon dioxide while assigning negative values of oxygen.The density of carbon dioxide increases faster than the density of oxygen goes away since the molecularwight is higher for carbon dioxide. Here, there is an increase in gases species which means that more energy

39

has to be added to heat up the system than in a real scenario. The magnitude of this error was investigatedhere. Consider the case in which the initial temperature is 15◦C. The initial value of ρO2cpO2

+ ρCO2cpCO2is

0.12 kJ/(m3 ·K). After 310 days of storage the value have increased to 1.02 kJ/(m3 ·K). The initial value ofρDMcDM is 533 kJ/(m3 ·K), the value decreases to 524.68 kJ/(m3 ·K) after 310 days of storage. The errordiscussed here is negligible since 524.68� 1.02.

40

Figure 7.13: Dimensions of the piles as well as measured positions within the piles.

7.6 Appendix E - Field study result

The experimental data presented here is from a field study performed at Nykvarn, Sweden between Februaryto August in 2017. The study was conducted by Erik Anerud from SLU. Here, data is shown from two stacks.One of these stack were covered while the other one was kept uncovered. These stacks were composed ofstemwood and they were built against a wall, the maximum height of the piles were 5.5 m. Measurementsare shown from three different positions within the piles. The first position had a height of 1.5 m, the secondwas placed 3.0 m above the ground and the third position had a height of 4.5 m. The piles and the positionsare illustrated in figure 7.13.

Figure 7.14 shows the percentage of degraded substrate after 30, 60, 120 and 180 days for the uncovered andcovered pile. The shown data is produced by three sample points. The biggest degradation happened withinthe first 30 days of storage. Lower degradation percentages were measured in the covered pile compared tothe uncovered pile. Generally, position 1 experienced the lowest degradation.

Figure 7.15 shows the moisture content of the wood i.e the weight fraction of liquid water after 0, 30, 60,120 and 180 days of storage. Data is presented for the uncovered and covered pile. The initial data pointfor moisture was produced by 12 sample points while the rest were produced by three sample points. Hereit can be seen that the moisture level varies less in the covered pile than in the uncovered pile. The initialmoisture content were around 35 wt%. The fraction of liquid water never dropped below the fibre saturationpoint (25 wt%).

Figure 7.16 shows the temperature evolution in the stack during the first 30 days of storage as well as theambient temperature during this time. The initial temperature was close to 47◦C. Position 2 and 3 showgreater increase in temperature than position 1. Data for position 1 is less consistent than for the othertwo positions. The temperature profile in position 2 and 3 are similar to each other. The lowest recordedtemperature in position 3 was 9.9◦C, this temperature was measured during day 29. The highest temperaturein position 3 was recorded after 11 days of storage, the temperature reached 156.4◦C. The lowest temperaturein position 2 was measured to be 10.4◦C after 24 days. The temperature reached its peak at 143◦C duringday 12 in position 2.

Figure 7.17 shows the ambient temperature and the temperature profile in the stack during the first 30 daysof storage for the covered pile. The temperature profiles are similar in all three positions. The temperaturefluctuates between 40-70◦C in all three positions.

41

Figure 7.14: Percentage of degraded biomass.

Figure 7.15: The humidity inside the stacks.

42

Figure 7.16: Temperature profiles in the uncovered stack.

Figure 7.17: Temperature profiles in the covered stack.

43

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